1. Field of the Invention
The present disclosure relates to the field of tomographic reconstruction and more particularly to the reconstruction of a sequence of 3D image(s) describing an object to be imaged by means of a contrast product.
2. Description of the Prior Art
Tomography allows making images of slices of a region of interest of an object by acquiring projections.
FIG. 1 schematically illustrates the acquisition of 2D images of an organ and the tomographic reconstruction of a 3D image of this organ. Reconstruction of a 3D image by tomography consists of emitting X-rays 10 from a source to the organ 12, the X-rays being emitted according to different angulations lε{1, . . . , L} which define the trajectory Tr of the source (commonly rotation, also known as spin).
After having passed through the organ 12, the X-rays 10 are detected by a detector 13 to form a set of 2D projections. There are as many 2D projections acquired as relevant angulations (or L projections for the trajectory). Acquisition is carried out by a detector (not shown) located opposite the source of X-rays 11. The detector may be, for example, a digital camera.
One application of tomography is the detection and characterisation of a lesion in an organ, for example, stenosis in a vessel of a patient.
The acquired 2D projections are used to reconstruct a 3D image of the object. This 3D image is more precisely a 3D map of the coefficients of attenuation to X-rays of the traversed medium. Using this map, the radiological practitioner interprets this image as a function of the differences in contrast observed.
An iterative 3D reconstruction process is known. This process is based on a discrete and matricial expression of the problem of tomographic reconstruction. Such a process is carried out in a processing unit of a medical imaging system. More precisely, the problem is modelled by the following equation:Rf=p,where p is the set of L projections acquired, R is a projection operator which models the tomographic imaging system and its trajectory of acquisition of L projections p, and f is the 3D image of the object to be reconstructed.
The problem of tomographic reconstruction is determining f by knowing p and R. A known solution to the equation mentioned hereinabove is the resolution of the following criterion:
         {                                                      Q              ⁡                              (                g                )                                      =                                          1                2                            ⁢                                                                                                            R                      ⁢                                                                                          ⁢                      g                                        -                    p                                                                    2                2                                                                                                    g              *                        =                                                            arg                  ⁢                                                                          ⁢                  min                                g                            ⁢                                                          ⁢                              Q                ⁡                                  (                  g                  )                                                                        where ∥ ∥2 symbolises the Euclidian standard said L2.
Minimization of the criterion Q(g) relative to g gives good results (g*≈f) when the set of projections p is such that L is large (typically a few hundreds) and when the set of L angulations covers at least 180° degrees. These conditions are commonly verified when the organ is static during the time necessary to effect a rotation of the imaging system.
A problem arises in getting an image of the blood vessels which do not show a marked difference in contrast relative to the surrounding tissue. It is therefore necessary to inject a so-called “contrast” product, for example an iodised product, into the vessels so as to make them more opaque to X-rays and allow them to be displayed as much in 2D projections as in associated 3D reconstructions. The image of the vessels alone is obtained by subtracted angiography where two acquisitions are made: one without contrast product, known as “mask” and noted pM, and a second one, known as “opacified” and noted pO, identical in terms of geometry, but after injection of the contrast product. The order in which these acquisitions are done does not matter. The image of the vessels in the images is obtained by opacified subtraction minus mask. Subtracted tomographic acquisition occurs therefore as the succession of two tomographic acquisitions, masked and opacified, such that an image of the acquisition mask (same geometry) allowing subtraction corresponds to each image of the opacified acquisition.
The 3D mask images, noted fM, opacified, noted fO, and subtracted, noted fS, are respectively defined as the solutions to the problems RfM=pM, RfO=pO and RfS=pO−pM. They are linked by the relationship fS=fO−fM and by the symbol R common to all three problems, which translates the geometric identity of the spins and consequently the possibility of subtraction of data pO−pM.
The contrast product dilutes rapidly in the blood flow. The maximal rotation speed of the tomographic system is generally used to limit the volume of contrast product necessary for opacified acquisition. The angular sampling conditions of the tomography also involve obtaining a few hundreds of images by acquisition, commonly 600. Angiography systems are however limited in speed of rotation, commonly 40°/s, and in image rate, commonly 50 Hz, such that the total number of images acquired, for example 250, is sufficient for the display of strong contrasts such as bones and opacified vessels, but insufficient for weak contrasts, such as soft tissue and perfused tissue. It is said that contrast resolution is limited by sampling. The 3D image subtracted from the contrast product alone (opacified vessels and perfused tissue) suffers under the same limitations of sampling, although it is the result of two acquisitions, simply because these two acquisitions reproduce the same limited sampling enabling subtraction of 2D projections instead of being complementary to enable an increase in contrast resolution.
Reference is now made to the general case where the acquisition mask is modelled by the operator RM, and acquisition opacified by the operator RO. The 3D images fM, and fO are respectively defined by RMfM=pM and ROfO=pO and are linked by the relationship fS=fO−fM. As the hypothesis RM=RO, is no longer necessarily done, the subtraction of data can no longer be written; generation of the subtracted 3D image no longer occurs except by subtraction of the opacified 3D image, reconstruction of opacified spin at rapid rotation (defined by RO), and of the 3D image mask, reconstruction of a spin mask at rapid rotation, or even of any other spin enabling reconstruction of the object of interest without injection of contrast product (defined by RM). In particular, spin at slower rotation will accumulate the number of projections necessary for detection of weak contrasts of soft tissue in the 3D image mask. This case corresponds however to an increase in the total number of projections acquired and therefore of the dose of X-rays associated with examination, without consequence for contrast resolution of the opacified 3D image which is not improved for perfused tissue.
Embodiments of the present invention consist of simultaneously using the two mask and opacified acquisitions to reconstruct the associated opacified and subtracted 3D mask images in order to reduce the number of projections necessary for detection of weak contrasts in the reconstructed 3D images. For this, it is based on temporal interpretation of acquisition with injection of contrast product in considering two temporal points: tO for the injection and tM for the mask. It hypothesises that the time changes caused by injection of contrast product are compressible. The time series to be reconstructed is therefore constituted by the vector {right arrow over (f)}={f(tO),f(tM)}={fO,fM} for which a time transform {right arrow over (h)}=Ht{right arrow over (f)}={hα,hδ} can be defined where the constituents hα and hδ are 3D images and such that one at least of the constituents of Ht{right arrow over (f)} is parsimonious.
This hypothesis proposes a method of reconstruction for compensating sub-sampling of variations linked to injection, and therefore more particularly improving reconstruction of the subtracted 3D image. A corollary to the hypothesis of compressibility is that the parts not affected by the contrast product are redundant in the acquisitions, and must therefore be determined by the set of available data {right arrow over (p)}={p(tO),p(tM)}={pO,pM} according to the relationship R{right arrow over (f)}={right arrow over (p)} with R diagonal operator by block, where each block of the diagonal models spin, or R=diag{R(tM),R(tO)}=diag{RM,RO}. So, without making a hypothesis of compressibility on the mask and opacified 3D images themselves, improved reconstruction of their common parts is obtained because of Ht. A novel consequence of this analysis is that it is then advantageous to take R(tM)#R(tO) to make the two acquisitions as complementary as possible.
In particular, if R(tM) samples a circular trajectory with an angular pitch δθ, and if R(tO) samples a circular trajectory with the same angular pitch δθ, they will be offset by δθ/2 in embodiments of the present invention so that the operator R=diag{R(tO),R(tM)} corresponds to a sampling of a circular trajectory with an angular pitch of δθ/2. It is evident that angular sampling for the same number of projections is doubled (and therefore the same dose of X-rays) relative to the common case where R(tM)=R(tO).